The exhaust gas of diesel engines contains more or less high concentrations of soot particles which are pollutive or even are rated as being a potential hazard to health when present in the breathing air in higher concentrations. This is the reason why endeavors have been made for some time to decontaminate the exhaust gases of diesel engines by removing the soot particles at least to a large extent. As technically most promising measure in the respect, exhaust gas soot filters have been conceived which are designed in their porosity such that they largely retain the soot particles from the exhaust gas flowing therethrough. These soot filters often consist of ceramic material because of the required temperature and strength needed with respect to the usual exhaust gas temperatures of diesel engines. These soot filters also have the tendency of becoming clogged with prolonged time of operation. It was hoped that the soot particles caught in the soot filter would be burnt off virtually to the same extent in which new particles accumulate, and in particular in relation with higher output conditions of the respective diesel engine. However, it has become evident that this hope is not fulfilled at least with a multiplicity of diesel engines. In particular such engines which are not often enough operated in operating conditions with relatively high exhaust gas temperatures. Instead, a constantly increasing accumulation of soot particles in the soot filter takes place which, thus, reaches in increasing manner a condition of undesirably high exhaust gas flow resistance.